Since the discovery of sophisticated fully polynomial randomized algorithms for a range of #P problems (Karzanov et al., 1991; Jerrum et al., 2001; Wilson, 2004), theoretical work on approximate inference in combinatorial spaces has focused on Markov chain Monte Carlo methods. Despite their strong theoretical guarantees, the slow running time of many of these randomized algorithms and the restrictive assumptions on the potentials have hindered the applicability of these algorithms to machine learning. Because of this, in applications to combinatorial spaces simple exact models are often preferred to more complex models that require approximate inference (Siepel et al., 2004). Variational inference would appear to provide an appealing alternative, given the success of variational methods for graphical models (Wainwright et al., 2008); unfortunately, however, it is not obvious how to develop variational approximations for combinatorial objects such as matchings, partial orders, plane partitions and sequence alignments. We propose a new framework that extends variational inference to a wide range of combinatorial spaces. Our method is based on a simple assumption: the existence of a tractable measure factorization, which we show holds in many examples. Simulations on a range of matching models show that the algorithm is more general and empirically faster than a popular fully polynomial randomized algorithm. We also apply the framework to the problem of multiple alignment of protein sequences, obtaining state-of-the-art results on the BAliBASE dataset (Thompson et al., 1999).

How much information does a neural population convey about a stimulus? Answers to this question are known to strongly depend on the correlation of response variability in neural populations. These noise correlations, however, are essentially immeasurable as the number of parameters in a noise correlation matrix grows quadratically with population size. Here, we suggest to bypass this problem by imposing a parametric model on a noise correlation matrix. Our basic assumption is that noise correlations arise due to common inputs between neurons. On average, noise correlations will therefore reflect signal correlations, which can be measured in neural populations. We suggest an explicit parametric dependency between signal and noise correlations. We show how this dependency can be used to fill the gaps" in noise correlations matrices using an iterative application of the Wishart distribution over positive definitive matrices. We apply our method to data from the primary somatosensory cortex of monkeys performing a two-alternative-forced choice task. We compare the discrimination thresholds read out from the population of recorded neurons with the discrimination threshold of the monkey and show that our method predicts different results than simpler, average schemes of noise correlations."

When working with network datasets, the theoretical framework of detection theory for Euclidean vector spaces no longer applies. Nevertheless, it is desirable to determine the detectability of small, anomalous graphs embedded into background networks with known statistical properties. Casting the problem of subgraph detection in a signal processing context, this article provides a framework and empirical results that elucidate a detection theory" for graph-valued data. Its focus is the detection of anomalies in unweighted, undirected graphs through L1 properties of the eigenvectors of the graph’s so-called modularity matrix. This metric is observed to have relatively low variance for certain categories of randomly-generated graphs, and to reveal the presence of an anomalous subgraph with reasonable reliability when the anomaly is not well-correlated with stronger portions of the background graph. An analysis of subgraphs in real network datasets confirms the efficacy of this approach."

To understand the relationship between genomic variations among population and complex diseases, it is essential to detect eQTLs which are associated with phenotypic effects.However, detecting eQTLs remains a challenge due to complex underlying mechanisms and the very large number of genetic loci involved compared tothe number of samples. Thus, to address the problem, it is desirable to take advantage of the structure of the data and prior information about genomic locations such as conservation scores and transcription factor binding sites. In this paper, we propose a novel regularized regression approach for detecting eQTLs which takes into account related traits simultaneously while incorporating many regulatory features. We first present a Bayesian network for a multi-task learning problem that includes priors on SNPs, making it possible to estimate the significance of each covariate adaptively. Then we find the maximum a posteriori (MAP) estimation of regression coefficients and estimate weights of covariates jointly. This optimization procedure is efficient since it can be achieved by using aprojected gradient descent and a coordinate descent procedure iteratively. Experimental results on simulated and real yeast datasets confirm that our model outperforms previous methods for finding eQTLs.

Activity of a neuron, even in the early sensory areas, is not simply a function of its local receptive field or tuning properties, but depends on global context of the stimulus, as well as the neural context. This suggests the activity of the surrounding neurons and global brain states can exert considerable influence on the activity of a neuron. In this paper we implemented an L1 regularized point process model to assess the contribution of multiple factors to the firing rate of many individual units recorded simultaneously from V1 with a 96-electrode "Utah" array. We found that the spikes of surrounding neurons indeed provide strong predictions of a neuron's response, in addition to the neuron's receptive field transfer function. We also found that the same spikes could be accounted for with the local field potentials, a surrogate measure of global network states. This work shows that accounting for network fluctuations can improve estimates of single trial firing rate and stimulus-response transfer functions.

Feature selection is an important component of many machine learning applications. Especially in many bioinformatics tasks, efficient and robust feature selection methods are desired to extract meaningful features and eliminate noisy ones. In this paper, we propose a new robust feature selection method with emphasizing joint ℓ2,1-norm minimization on both loss function and regularization. The ℓ2,1-norm based loss function is robust to outliers in data points and the ℓ2,1-norm regularization selects features across all data points with joint sparsity. An efficient algorithm is introduced with proved convergence. Our regression based objective makes the feature selection process more efficient. Our method has been applied into both genomic and proteomic biomarkers discovery. Extensive empirical studies were performed on six data sets to demonstrate the effectiveness of our feature selection method.

We study repeated zero-sum games against an adversary on a budget. Given that an adversary has some constraint on the sequence of actions that he plays, we consider what ought to be the player's best mixed strategy with knowledge of this budget. We show that, for a general class of normal-form games, the minimax strategy is indeed efficiently computable and relies on a random playout" technique. We give three diverse applications of this algorithmic template: a cost-sensitive "Hedge" setting, a particular problem in Metrical Task Systems, and the design of combinatorial prediction markets."

We define a copula process which describes the dependencies between arbitrarily many random variables independently of their marginal distributions. As an example, we develop a stochastic volatility model, Gaussian Copula Process Volatility (GCPV), to predict the latent standard deviations of a sequence of random variables. To make predictions we use Bayesian inference, with the Laplace approximation, and with Markov chain Monte Carlo as an alternative. We find our model can outperform GARCH on simulated and financial data. And unlike GARCH, GCPV can easily handle missing data, incorporate covariates other than time, and model a rich class of covariance structures.

We propose a general framework to online learning for classification problems with time-varying potential functions in the adversarial setting. This framework allows to design and prove relative mistake bounds for any generic loss function. The mistake bounds can be specialized for the hinge loss, allowing to recover and improve the bounds of known online classification algorithms. By optimizing the general bound we derive a new online classification algorithm, called NAROW, that hybridly uses adaptive- and fixed- second order information. We analyze the properties of the algorithm and illustrate its performance using synthetic dataset.

Conventional dynamic Bayesian networks (DBNs) are based on the homogeneous Markov assumption, which is too restrictive in many practical applications. Various approaches to relax the homogeneity assumption have therefore been proposed in the last few years. The present paper aims to improve the flexibility of two recent versions of non-homogeneous DBNs, which either (i) suffer from the need for data discretization, or (ii) assume a time-invariant network structure. Allowing the network structure to be fully flexible leads to the risk of overfitting and inflated inference uncertainty though, especially in the highly topical field of systems biology, where independent measurements tend to be sparse. In the present paper we investigate three conceptually different regularization schemes based on inter-segment information sharing. We assess the performance in a comparative evaluation study based on simulated data. We compare the predicted segmentation of gene expression time series obtained during embryogenesis in Drosophila melanogaster with other state-of-the-art techniques. We conclude our evaluation with an application to synthetic biology, where the objective is to predict a known regulatory network of five genes in Saccharomyces cerevisiae.